sin(x+45)=2cos(x+45)

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Solution for sin(x+45)=2cos(x+45) equation:


Simplifying
sin(x + 45) = 2cos(x + 45)

Reorder the terms:
ins(45 + x) = 2cos(x + 45)
(45 * ins + x * ins) = 2cos(x + 45)
(45ins + insx) = 2cos(x + 45)

Reorder the terms:
45ins + insx = 2cos(45 + x)
45ins + insx = (45 * 2cos + x * 2cos)
45ins + insx = (90cos + 2cosx)

Solving
45ins + insx = 90cos + 2cosx

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Reorder the terms:
-90cos + -2cosx + 45ins + insx = 90cos + 2cosx + -90cos + -2cosx

Reorder the terms:
-90cos + -2cosx + 45ins + insx = 90cos + -90cos + 2cosx + -2cosx

Combine like terms: 90cos + -90cos = 0
-90cos + -2cosx + 45ins + insx = 0 + 2cosx + -2cosx
-90cos + -2cosx + 45ins + insx = 2cosx + -2cosx

Combine like terms: 2cosx + -2cosx = 0
-90cos + -2cosx + 45ins + insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-90co + -2cox + 45in + inx) = 0

Subproblem 1

Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing i to the left, all other terms to the right. Add '-1s' to each side of the equation. s + -1s = 0 + -1s Remove the zero: 0 = -1s Simplifying 0 = -1s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-90co + -2cox + 45in + inx)' equal to zero and attempt to solve: Simplifying -90co + -2cox + 45in + inx = 0 Solving -90co + -2cox + 45in + inx = 0 Move all terms containing i to the left, all other terms to the right. Add '90co' to each side of the equation. -90co + -2cox + 45in + 90co + inx = 0 + 90co Reorder the terms: -90co + 90co + -2cox + 45in + inx = 0 + 90co Combine like terms: -90co + 90co = 0 0 + -2cox + 45in + inx = 0 + 90co -2cox + 45in + inx = 0 + 90co Remove the zero: -2cox + 45in + inx = 90co Add '2cox' to each side of the equation. -2cox + 45in + 2cox + inx = 90co + 2cox Reorder the terms: -2cox + 2cox + 45in + inx = 90co + 2cox Combine like terms: -2cox + 2cox = 0 0 + 45in + inx = 90co + 2cox 45in + inx = 90co + 2cox The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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